Several different issues have been mentioned here. It's very true that when you double the output power of an amp, you don't change its loudness by much, but you do change its headroom and tone. Jimi Hendrix, so we're told, is an example of someone who really used all 100W of his Marshalls to get the tone and clarity he needed for what he was doing. There's a story that when he was recording at the BBC studios in Langham Place, London, they could still hear his guitar in the building several studios away!
And then there's also the effect of moving lots of air at extremely high volume levels. Eric Johnson, for example, used to experiment with the sound of very loud pressure waves, by playing high power amps in small rooms. Now of course, his hearing is damaged, and IIRC he can no longer hear high frequencies. Such a pity for someone who used to be known for chasing the ultimate guitar tones. I'm sure that if Hendrix was still alive today, his ears would be pretty well shot too - if not his brain.
People may wonder why a 100W, running at half power or using half its power tubes, will sound different to a 50W of exactly the same family. The difference is that the 100W amp has bigger transformers, so that the amp's tone will be bigger and bolder, even when running on half the power tubes. Due to the reduced load, the voltages in the 100W amp will also tend to rise above their normal level, providing a bit more headroom than a regular 50W.
It is true that Hiwatt amps were designed somewhat like high-powered hi-fi amps for maximum loud and clean operation. Guitar amps didn't get mic'ed through the PA in those days, and so they had to hold up on their own, which made Hiwatts ideal for the job. Like Brent said, they also make great bass amps, which IMO is for the same reason. Both John Entwhistle and Roger Glover come to mind right away as big into Hiwatts for their bass rigs. But again like Brent says, Hiwatts eventually break up with a beautiful growl. If you listen to the Who much, you can hear how Townshend overdrives his Hiwatts. So our aim is to get this signature growling breakup at safe(ish) volume levels.
So with the "triwatt" (which is not the amp's official name BTW for obvious legal reasons), the aim is to produce tone and breakup characteristics that are similar to a 100W, or at least a 50W Hiwatt amp, but without causing terminal ear damage or killing small birds flying nearby. While we know scientifically, it is impossible to produce a 100% accurate clone of the same sound in a lower power amp, we still intend to get pretty darn close to it.
PS: My own personal "go to" amp is an 18W Lite. The sweet, grinding overdriven tones from that amp are sheer bliss!